In §REF , we turn our attention to what happens when (QiS) and REF  hold, but REF  fails. In this case we much perform partial desingularisations as in [1]} for the reductive groups \(R^{(i)}\)  until we achieve REF  on the blown up space \(\widehat{X}\) , whilst also preserving (QiS) and REF  (see Proposition REF ). Then, in Proposition REF  we simply apply Proposition REF  to \(\widehat{X}\)  to deal with this case. Finally in \(§\)REF  we deal with the case when REF  fails by performing a blow-up sequence concerning unipotent stabilisers as described in \(§\)REF , which is based on an earlier arXiv version of [2]}. To achieve our result, we must avoid the bad situation where the whole minimal weight space is blown up at any stage, and this is where we use the assumption (WUU) to complete the proof of Theorem REF .
